Related Experiment Video
Updated: Sep 6, 2025

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
Published on: August 30, 2013
Phase space partition with Koopman analysis
Cong Zhang1, Haipeng Li1, Yueheng Lan1
1School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China.
Abstract:
Symbolic dynamics is a powerful tool to describe topological features of a nonlinear system, where the required partition, however, remains a challenge for some time due to the complications involved in determining the partition boundaries. In this article, we show that it is possible to carry out interesting symbolic partitions for chaotic maps based on properly constructed eigenfunctions of the finite-dimensional approximation of the Koopman operator. The partition boundaries overlap with the extrema of these eigenfunctions, the accuracy of which is improved by including more basis functions in the numerical computation. The validity of this scheme is demonstrated in well-known 1D and 2D maps.
Related Concept Videos
Extraction: Partition and Distribution Coefficients
For extracting a solute from an aqueous phase into an...
State Space Representation
Consider an RLC circuit, a...
Transfer function and Bode Plots-II
State Space to Transfer Function
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
Transfer Function to State Space
In an...
¹H NMR: Complex Splitting
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied...

